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Transformations between reference frames play a crucial role in our understanding of physical processes. In practice, reference frames are realised by physical systems, which are standardly treated as classical. However, assuming that every physical system is ultimately quantum, it is interesting to ask how a theory of transformations wrt quantum reference frames would look like, and what implications it would have for our description of spacetime. Recently, there has been a lot of effort towards developing a quantum generalisation of reference frame transformations, unveiling novel phenomena that are absent in the classical treatment of reference frames. Here, we develop a first-principles framework for quantum reference frame transformations which clarifies important conceptual issues of previous treatments. Based on the algebra of relative observables between a system and a reference frame, our operational perspective leads naturally to a mixed-state approach (incoherent twirling), in contrast to current pure-state approaches (coherent twirling). Within our framework, the full invariant quantum subsystem contains not only the algebra of relative observables between the system and the reference frame but also an “extra particle,” related to the invariant degrees of freedom of the reference frame itself. Importantly, this extra particle contains information about the “quantumness” of the reference frame and is essential to the unitarity of quantum reference frame transformations. Our approach is general, in the sense that it can be applied to a vast set of symmetry groups and to any type of system. We illustrate the physical meaning of the concepts developed by analysing quantum reference frame transformations with respect to the (centrally extended) Galilei group.

"We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability distribution arises from the Born rule and which has a clear physical interpretation. The same procedure can be employed to measure the ""time at which some event happens"" for arbitrary events (and not just specifically for the arrival time of a particle). This talk is based on the paper: L. Maccone, K. Sacha, Quantum measurements of time, Phys. Rev. Lett. 124, 110402 (2020)."

I will sketch how the perspective-neutral approach to (quantum) frame covariance brings together some recent developments on dynamical reference frames in quantum foundations, gauge theories and gravity. The survey will touch on spatial frames, quantum clocks and the problem of time, edge modes, and the relativity of subsystems.

"We propose a realist completion of quantum mechanics, in the sense of a complete description of individual events. The proposed fundamental theory assumes that time, events, causal structure, momentum and energy are fundamental. But space and the wave function are emergent. The beables of the theory are the views of the events, which are a subset of their causal pasts. Thus, this theory asserts that the universe is a causal network of events, which consists of partial views of itself as seen by looking backwards from each event. The theory is based on a simple action principle, which extremizes the variety of the universe, which is a measure of the diversity of its partial views. The Schroedinger equation is derived, while to higher order, there are computable corrections, non-linear in the wave function, from which new physical effects may be predicted. Finally, a relativistic version is sketched, in wqhich the views are built on the celestial sphere. "

Time cannot be both absolute (as in quantum mechanics) and dynamical (as in general relativity). I present general arguments for the absence of time at the most fundamental level of quantum gravity. I discuss possible concepts that could replace it and present the recovery of standard time as an approximate concept. My discussion is restricted to quantum geometrodynamics, but I argue for the validity of my conclusions beyond that scheme.

I will present a quantum gravity approach based on a Lorentzian path integral for quantum geometries. The properties of quantum space time can be measured using geometric operators. This allows also to discuss fluctuations of causal structure as well as violations of (micro-) causality. I will explain how the Lorentzian path integral comes with various options regarding which quantum space times to sum over: e.g. whether to include causality violations or not, or whether to allow also for space times with Euclidean signatures in Lorentzian path integrals. I will sketch some consequences for the resulting theories.

Time Reversal T is usually discussed in the traditional framework of quantum mechanics in which T is represented by an anti-unitary operator. But quantum gravity may well need generalization of standard quantum mechanics which may not preserve even its linear structure, let alone the unitarity of dynamics and anti-unitarity of T. Then the currently used arguments to conclude that T violation is a fundamental aspect of Nature will break down. Fortunately, it turns out that one can analyze the T-violation experiments in a much more general setting, of which classical and quantum mechanics are special cases. The setting does not require a Hilbert space, or linearity of either dynamics or symmetry operations such as T. Nonetheless, somewhat surprisingly, one would still be to use the current experiments to conclude that there is T violation at a fundamental level under rather minimal assumptions on the structure of the final quantum gravity theory.

In physics, a reference frame is an abstract coordinate system that specifies observations within that frame. While quantum states depend on the choice of reference frame, the form of physical laws is assumed to be covariant. Recently, it has been proposed to consider reference frames as physical systems and as such assume that they obey quantum mechanics. In my talk, I will present recent results in the field of "quantum reference frames" (QRF). In particular, I will formulate the covariance of dynamical physical laws with respect to non-relativistic QRF transformations and show how relativistic QRFs can be used to solve a long-standing problem in relativistic quantum information or to address typical quantum gravity scenarios.